सिद्ध करे
`tan^(-1)x +tan^(-1)""(2x)/(1-x^(2)) =tan^(-1)((3x-x^(3))/(1-3x^(2))), x^(2) lt(1)/(3).`

Explanation

माना कि `tan^(-1) x = theta, " " therefore x = tan theta`
`L.H.S. = tan^(-1) x + tan^(-1) ""(2x)/(1-x^(2))`
` = theta + tan^(-1)((2tan theta)/(1-tan^(2) theta))`
` = theta + tan^(-1) (tan 2 theta)`
` = theta + 2theta = 3 theta" "...(1)`
`R.H.S. = tan^(-1) ((3x-x^(3))/(1-3x^(2)))`
` = tan^(-1)((3 tan theta -tan^(3) theta)/(1-3 tan^(2) theta))`
` = tan^(-1) (tan 3theta) = 3theta" "...(2)`
समीकरण (1) और (2) से
L.H.S. = R.H.S.